Quantum Field Theory and Quantum Topology - Jørgen Andersen
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- čas přidán 8. 08. 2016
- Serious Science - serious-science.org
Mathematician Jørgen Andersen on topological quantum field theory, path integrals, and quantization of moduli spaces
serious-science.org/quantum-fi... - Věda a technologie
This seems very promising. There is a way to see quantum mechanics as a kind of complexification (read: spacetime geometrization) of statistical mechanics, so dynamical rather that equilibrium. The partition function is the sum over topologies of a "complex" (read: real spacetime geometric) exponential in QM, whereas in SM it's a real exponential (read: real but equilibrium). Turok and Boyle show the correct interpretation is not of a Wick rotation, but rather use Picard--Lefschetz theory to retain Lorentzian path integrals which preserves interference. Lisi, Baez and Pollard call the Feynman partition function a "reservoir of actions", entropy is analogous to "quantropy". Again, the distinction is that quantropy can model (account for) interference, entropy cannot.
There is a nice way to relate this to Anderson's vision: the "quantum topology" is just gravity with non-trivial topology around the Planck scale. It is classical GR really, but with closed timelike curves (at the Planck scale). It only becomes "quantum" because of the CTC effects, nothing else. The CTCs are what allow matter to "explore" or "sample" in Jørgen's words, "all possible paths". Except the key realization is nature only samples, it does not need to literally take all possible paths (so the parallel worlds or Everettian ideas are wrong, they are an unphysical extreme limit of the natural processes).
Beautiful math conceptual art I agree.
Great explanation
Amazing!
wow... so not only do physics and math go both ways, but one discovery in either can cascade far into both?
+++THUNDER
what?
One field, 3 field modalities. We’ve been doing this since the 50’s. Yes the either is a thing and measured as Z. Yet fields are multiplicative, and inverse, not additive. The things you are not taught.
We are the shadowworld.
qwq
Agreed I'm a layman however, agree coming to the same conclusion a while ago that the gap between relativity and quantum is going to be bridged through the invention of new math.